Calibration of a three-state cell death model for cardiomyocytes and its application in radiofrequency ablation.

Objective.Thermal cellular injury follows complex dynamics and subcellular processes can heal the inflicted damage if insufficient heat is administered during the procedure. This work aims to the identification of irreversible cardiac tissue damage for predicting the success of thermal treatments.Approach.Several approaches exist in the literature, but they are unable to capture the healing process and the variable energy absorption rate that several cells display. Moreover, none of the existing models is calibrated for cardiomyocytes. We consider a three-state cell death model capable of capturing the reversible damage of a cell, we modify it to include a variable energy absorption rate and we calibrate it for cardiac myocytes.Main results.We show how the thermal damage predicted by the model response is in accordance with available data in the literature on myocytes for different temperature distributions. When coupled with a computational model of radiofrequency catheter ablation, the model predicts lesions in agreement with experimental measurements. We also present additional experiments (repeated ablations and catheter movement) to further illustrate the potential of the model.Significance.We calibrated a three-state cell death model to provide physiological results for cardiac myocytes. The model can be coupled with ablation models and reliably predict lesion sizes comparable to experimental measurements. Such approach is robust for repeated ablations and dynamic catheter-cardiac wall interaction, and allows for tissue remodelling in the predicted damaged area, leading to more accurate in-silico predictions of ablation outcomes.

Blood flow but not cannula positioning influences the efficacy of Veno-Venous ECMO therapy.

Despite being vital in treating intensive-care patients with lung failure, especially COVID-19 patients, Veno-Venous Extra-Corporeal Membrane Oxygenation does not exploit its full potential, leaving ample room for improvement. The objective of this study is to determine the effect of cannula positioning and blood flow on the efficacy of Veno-Venous Extra-Corporeal Membrane Oxygenation, in particular in relationship with blood recirculation. We performed 98 computer simulations of blood flow and oxygen diffusion in a computerized-tomography-segmented right atrium and venae cavae for different positions of the returning and draining cannulae and ECMO flows of 3 L/min and [Formula: see text]. For each configuration we measured how effective Veno-Venous Extra-Corporeal Membrane Oxygenation is at delivering oxygen to the right ventricle and thus to the systemic circulation. The main finding is that VV-ECMO efficacy is largely affected by the ECMO flow (global peak blood saturation: [Formula: see text]; average inter-group saturation gain: 9 percentage points) but only scarcely by the positioning of the cannulae (mean saturation ± standard deviation for the 3 L/min case: [Formula: see text]; for the [Formula: see text] case: [Formula: see text]). An important secondary outcome is that recirculation, more intense with a higher ECMO flow, is less detrimental to the procedure than previously thought. The efficacy of current ECMO procedures is intrinsically limited and fine-tuning the positions of the cannulae, risking infections, offers very little gain. Setting a higher ECMO flow offers the biggest benefit despite mildly increasing blood recirculation.

Oscillations in K(ATP) conductance drive slow calcium oscillations in pancreatic ß-cells.

ATP-sensitive K+ (K(ATP)) channels were first reported in the ß-cells of pancreatic islets in 1984, and it was soon established that they are the primary means by which the blood glucose level is transduced to cellular electrical activity and consequently insulin secretion. However, the role that the K(ATP) channels play in driving the bursting electrical activity of islet ß-cells, which drives pulsatile insulin secretion, remains unclear. One difficulty is that bursting is abolished when several different ion channel types are blocked pharmacologically or genetically, making it challenging to distinguish causation from correlation. Here, we demonstrate a means for determining whether activity-dependent oscillations in K(ATP) conductance play the primary role in driving electrical bursting in ß-cells. We use mathematical models to predict that if K(ATP) is the driver, then contrary to intuition, the mean, peak, and nadir levels of ATP/ADP should be invariant to changes in glucose within the concentration range that supports bursting. We test this in islets using Perceval-HR to image oscillations in ATP/ADP. We find that mean, peak, and nadir levels are indeed approximately invariant, supporting the hypothesis that oscillations in K(ATP) conductance are the main drivers of the slow bursting oscillations typically seen at stimulatory glucose levels in mouse islets. In conclusion, we provide, for the first time to our knowledge, causal evidence for the role of K(ATP) channels not only as the primary target for glucose regulation but also for their role in driving bursting electrical activity and pulsatile insulin secretion.

Impact of electrode tip shape on catheter performance in cardiac radiofrequency ablation.

Background: The role of catheter tip shape on the safety and efficacy of radiofrequency (RF) ablation has been overlooked, although differences have been observed in clinical and research fields. Objective: The purpose of this study was to analyze the role of electrode tip shape in RF ablation using a computational model. Methods: We simulated 108 RF ablations through a realistic 3-dimensional computational model considering 2 clinically used, open-irrigated catheters (spherical and cylindrical tip), varying contact force (CF), blood flow, and irrigation. Lesions are defined by the 50°C isotherm contour and evaluated by means of width, depth, depth at maximum width, and volume. Ablations are deemed as safe, critical (tissue temperature >90°C), and pop (tissue temperature >100°C). Results: Tissue-electrode contact is less for the spherical tip at low CF but the relationship is inverted at high CF. At low CF, the cylindrical tip generates deeper and wider lesions and a 4-fold larger volume. With increasing CF, the lesions generated by the spherical tip become comparable to those generated by the cylindrical tip. The 2 tips feature different safety profiles: CF and power are the main determinants of pops for the spherical tip; power is the main factor for the cylindrical tip; and CF has a marginal effect. The cylindrical tip is more prone to pop generation at higher powers. Saline irrigation and blood flow effect do not depend on tip shape. Conclusion: Tip shape determines the performance of ablation catheters and has a major impact on their safety profile. The cylindrical tip shows more predictable behavior in a wide range of CF values.

A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics.

Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.

Systematic Characterization of High-Power Short-Duration Ablation: Insight From an Advanced Virtual Model.

Background: High-power short-duration (HPSD) recently emerged as a new approach to radiofrequency (RF) catheter ablation. However, basic and clinical data supporting its effectiveness and safety is still scarce. Objective: We aim to characterize HPSD with an advanced virtual model, able to assess lesion dimensions and complications in multiple conditions and compare it to standard protocols. Methods: We evaluate, on both atrium and ventricle, three HPSD protocols (70 W/8 s, 80 W/6 s, and 90 W/4 s) through a realistic 3D computational model of power-controlled RF ablation, varying catheter tip design (spherical/cylindrical), contact force (CF), blood flow, and saline irrigation. Lesions are defined by the 50°C isotherm contour. Ablations are deemed safe or complicated by pop (tissue temperature >97°C) or charring (blood temperature >80°C). We compared HPSD with standards protocols (30-40 W/30 s). We analyzed the effect of a second HPSD application. Results: We simulated 432 applications. Most (79%) associated a complication, especially in the atrium. The three HPSD protocols performed similarly in the atrium, while 90 W/4 s appeared the safest in the ventricle. Low irrigation rate led frequently to charring (72%). High-power short-duration lesions were 40-60% shallower and smaller in volume compared to standards, although featuring similar width. A second HPSD application increased lesions to a size comparable to standards. Conclusion: High-power short-duration lesions are smaller in volume and more superficial than standards but comparable in width, which can be advantageous in the atrium. A second application can produce lesions similar to standards in a shorter time. Despite its narrow safety margin, HPSD seems a valuable new clinical approach.

Cardiac computational modelling.

Cardiovascular diseases currently have a major social and economic impact, constituting one of the leading causes of mortality and morbidity. Personalized computational models of the heart are demonstrating their usefulness both to help understand the mechanisms underlying cardiac disease, and to optimize their treatment and predict the patient's response. Within this framework, the Spanish Research Network for Cardiac Computational Modelling (VHeart-SN) has been launched. The general objective of the VHeart-SN network is the development of an integrated, modular and multiscale multiphysical computational model of the heart. This general objective is addressed through the following specific objectives: a) to integrate the different numerical methods and models taking into account the specificity of patients; b) to assist in advancing knowledge of the mechanisms associated with cardiac and vascular diseases; and c) to support the application of different personalized therapies. This article presents the current state of cardiac computational modelling and different scientific works conducted by the members of the network to gain greater understanding of the characteristics and usefulness of these models.

Glioma invasion and its interplay with nervous tissue and therapy: A multiscale model.

A multiscale mathematical model for glioma cell migration and proliferation is proposed, taking into account a possible therapeutic approach. Starting with the description of processes occurring at the subcellular level, the equation for the mesoscopic level is formulated and a macroscopic model is derived, via parabolic limit and Hilbert expansions in the moment equations. After the model set up and the study of the well-posedness of this macroscopic setting, we investigate the role of the fibers in the tumor dynamics. In particular, we focus on the fiber density function, with the aim of comparing some common choices present in the literature and understanding which differences arise in the description of the actual fiber density and orientation. Finally, some numerical simulations, based on real data, highlight the role of each modelled process in the evolution of the solution of the macroscopic equation.

Meta-modeling on detailed geography for accurate prediction of invasive alien species dispersal.

Invasive species are recognized as a significant threat to biodiversity. The mathematical modeling of their spatio-temporal dynamics can provide significant help to environmental managers in devising suitable control strategies. Several mathematical approaches have been proposed in recent decades to efficiently model the dispersal of invasive species. Relying on the assumption that the dispersal of an individual is random, but the density of individuals at the scale of the population can be considered smooth, reaction-diffusion models are a good trade-off between model complexity and flexibility for use in different situations. In this paper we present a continuous reaction-diffusion model coupled with arbitrary Polynomial Chaos (aPC) to assess the impact of uncertainties in the model parameters. We show how the finite elements framework is well-suited to handle important landscape heterogeneities as elevation and the complex geometries associated with the boundaries of an actual geographical region. We demonstrate the main capabilities of the proposed coupled model by assessing the uncertainties in the invasion of an alien species invading the Basque Country region in Northern Spain.

Clinical correlates of mathematical modeling of cortical spreading depression: Single-cases study.

INTRODUCTION: Considerable connections between migraine with aura and cortical spreading depression (CSD), a depolarization wave originating in the visual cortex and traveling toward the frontal lobe, lead to the hypothesis that CSD is underlying migraine aura. The highly individual and complex characteristics of the brain cortex suggest that the geometry might impact the propagation of cortical spreading depression. METHODS: In a single-case study, we simulated the CSD propagation for five migraine with aura patients, matching their symptoms during a migraine attack to the CSD wavefront propagation. This CSD wavefront was simulated on a patient-specific triangulated cortical mesh obtained from individual MRI imaging and personalized diffusivity tensors derived locally from diffusion tensor imaging data. RESULTS: The CSD wave propagation was simulated on both hemispheres, despite in all but one patient the symptoms were attributable to one hemisphere. The CSD wave diffused with a large wavefront toward somatosensory and prefrontal regions, devoted to pain processing. DISCUSSION: This case-control study suggests that the cortical geometry may contribute to the modality of CSD evolution and partly to clinical expression of aura symptoms. The simulated CSD is a large and diffuse phenomenon, possibly capable to activate trigeminal nociceptors and to involve cortical areas devoted to pain processing.

A computational model of open-irrigated radiofrequency catheter ablation accounting for mechanical properties of the cardiac tissue.

Radiofrequency catheter ablation (RFCA) is an effective treatment for cardiac arrhythmias. Although generally safe, it is not completely exempt from the risk of complications. The great flexibility of computational models can be a major asset in optimizing interventional strategies if they can produce sufficiently precise estimations of the generated lesion for a given ablation protocol. This requires an accurate description of the catheter tip and the cardiac tissue. In particular, the deformation of the tissue under the catheter pressure during the ablation is an important aspect that is overlooked in the existing literature, which resorts to a sharp insertion of the catheter into an undeformed geometry. As the lesion size depends on the power dissipated in the tissue and the latter depends on the percentage of the electrode surface in contact with the tissue itself, the sharp insertion geometry has the tendency to overestimate the lesion obtained, which is a consequence of the tissue temperature rise overestimation. In this paper, we introduce a full 3D computational model that takes into account the tissue elasticity and is able to capture tissue deformation and realistic power dissipation in the tissue. Numerical results in FEniCS-HPC are provided to validate the model against experimental data and to compare the lesions obtained with the new model and with the classical ones featuring a sharp electrode insertion in the tissue.

Transitions between bursting modes in the integrated oscillator model for pancreatic ß-cells.

Insulin-secreting ß-cells of pancreatic islets of Langerhans produce bursts of electrical impulses, resulting in intracellular Ca2+ oscillations and pulsatile insulin secretion. The mechanism for this bursting activity has been the focus of mathematical modeling for more than three decades, and as new data are acquired old models are modified and new models are developed. Comprehensive models must now account for the various modes of bursting observed in islet ß-cells, which include fast bursting, slow bursting, and compound bursting. One such model is the Integrated Oscillator Model (IOM), in which ß-cell electrical activity, intracellular Ca2+, and glucose metabolism interact via numerous feedforward and feedback pathways. These interactions can produce metabolic oscillations with a sawtooth time course or a pulsatile time course, reflecting very different oscillation mechanisms. In this report, we determine conditions favorable to one form of oscillations or the other, and examine the transitions between modes of bursting and the relationship of the transitions to the patterns of metabolic oscillations. Importantly, this work clarifies what can be expected in experimental measurements of ß-cell oscillatory activity, and suggests pathways through which oscillations of one type can be converted to oscillations of another type.

Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging.

Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.

Computational Modeling of Open-Irrigated Electrodes for Radiofrequency Cardiac Ablation Including Blood Motion-Saline Flow Interaction.

Radiofrequency catheter ablation (RFCA) is a routine treatment for cardiac arrhythmias. During RFCA, the electrode-tissue interface temperature should be kept below 80 °C to avoid thrombus formation. Open-irrigated electrodes facilitate power delivery while keeping low temperatures around the catheter. No computational model of an open-irrigated electrode in endocardial RFCA accounting for both the saline irrigation flow and the blood motion in the cardiac chamber has been proposed yet. We present the first computational model including both effects at once. The model has been validated against existing experimental results. Computational results showed that the surface lesion width and blood temperature are affected by both the electrode design and the irrigation flow rate. Smaller surface lesion widths and blood temperatures are obtained with higher irrigation flow rate, while the lesion depth is not affected by changing the irrigation flow rate. Larger lesions are obtained with increasing power and the electrode-tissue contact. Also, larger lesions are obtained when electrode is placed horizontally. Overall, the computational findings are in close agreement with previous experimental results providing an excellent tool for future catheter research.

Geometry Shapes Propagation: Assessing the Presence and Absence of Cortical Symmetries through a Computational Model of Cortical Spreading Depression.

Cortical spreading depression (CSD), a depolarization wave which originates in the visual cortex and travels toward the frontal lobe, has been suggested to be one neural correlate of aura migraine. To the date, little is known about the mechanisms which can trigger or stop aura migraine. Here, to shed some light on this problem and, under the hypothesis that CSD might mediate aura migraine, we aim to study different aspects favoring or disfavoring the propagation of CSD. In particular, by using a computational neuronal model distributed throughout a realistic cortical mesh, we study the role that the geometry has in shaping CSD. Our results are two-fold: first, we found significant differences in the propagation traveling patterns of CSD, both intra and inter-hemispherically, revealing important asymmetries in the propagation profile. Second, we developed methods able to identify brain regions featuring a peculiar behavior during CSD propagation. Our study reveals dynamical aspects of CSD, which, if applied to subject-specific cortical geometry, might shed some light on how to differentiate between healthy subjects and those suffering migraine.

Structuring targeted surveillance for monitoring disease emergence by mapping observational data onto ecological process.

An efficient surveillance system is a crucial factor in identifying, monitoring and tackling outbreaks of infectious diseases. Scarcity of data and limited amounts of economic resources require a targeted effort from public health authorities. In this paper, we propose a mathematical method to identify areas where surveillance is critical and low reporting rates might leave epidemics undetected. Our approach combines the use of reference-based susceptible-exposed-infectious models and observed reporting data; We propose two different specifications, for constant and time-varying surveillance, respectively. Our case study is centred around the spread of the raccoon rabies epidemic in the state of New York, using data collected between 1990 and 2007. Both methods offer a feasible solution to analyse and identify areas of intervention.

Numerical simulation of a susceptible-exposed-infectious space-continuous model for the spread of rabies in raccoons across a realistic landscape.

We introduce a numerical model for the spread of a lethal infectious disease in wildlife. The reference model is a Susceptible-Exposed-Infectious system where the spatial component of the dynamics is modelled by a diffusion process. The goal is to develop a model to be used for real geographical scenarios, so we do not rely upon simplifying assumptions on the shape of the region of interest. For this reason, space discretization is carried out with the finite element method on an unstructured triangulation. A diffusion term is designed to take into account landscape heterogeneities such as mountains and waterways. Numerical simulations are carried out for rabies epidemics among raccoons in New York state. A qualitative comparison of numerical results to available data from real-world epidemics is discussed.